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Fundamentals of Radio Astronomy
Lyle Hoffman, Lafayette College
ALFALFA Undergraduate Workshop
Union College, 2005 July 06
Outline• Sources in brief
• Radiotelescope components
• Radiotelescope characteristics
Useful TextsBurke & Graham-Smith, An Introduction to Radio AstronomyRohlfs, Tools of Radio AstronomyStanimirovic et al., Single-dish Radio Astronomy: Techniques and Applications
Blackbody Sources
• Peak in cm-wave radio requires very low temperature: mT = 0.2898 cm K
• Cosmic Microwave Background is about the only relevant blackbody source
• Ignored in most work – essentially constant source of static (same in all directions) and much weaker than static produced by instrumentation itself
Continuum Sources
• Due to relativistic electrons:
Synchrotron radiation
Bremsstrahlung
• Quasars, Active Galactic Nuclei, Pulsars, Supernova Remnants, etc.
• Used by ALFALFA for calibration
Spectral Line Sources
• Neutral hydrogen (H I ) spin-flip transition
• Recombination lines (between high-lying atomic states)
• Molecular lines (CO, OH, etc.)
• Doppler effect: frequency shift of spectral line due to relative motion of source and observer
• Closely related: redshift due to expansion of universe
• Customarily report “velocity” as
cz = c(fo-f)/f
• H I spectral line from galaxy shifted by expansion of universe (“recession velocity”) and broadened by rotation
Frequency
Radiotelescope Components
• Reflector(s)
• Feed horn(s)
• Low-noise amplifier
• Filter
• Downconverter
• IF Amplifier
• Spectrometer
Autocorrelation Spectrometer
• Special-purpose hardware computes autocorrelation function:
Rn = 1N [(tj)(tj+nt)]
where t is lag and is signal voltage; integer n ranges from 0 to (t f)-1 if frequency channels of width f are required
• Power spectrum is discrete Fourier transform (FFT) of Rn
Radiotelescope Characteristics
• Gain & effective area
• Beam, sidelobes, stray radiation
• Sensitivity, noise & integration time
• Polarization & Stoke’s parameters
Gain & effective area
• Received power Prec
• Flux (energy per unit area per unit time) S
• Effective area Aeff = Prec / S
• Gain G for transmitter is ratio of emitted flux in given direction to P/(4r2)
• Most emitted (received) within central diffraction max, angle ~ / D
• So G = 4Aeff / 2
Beam & sidelobes
• Essentially diffraction pattern of telescope functioning as transmitter
• Uniformly illuminated circular aperture: central beam & sidelobe rings
• Obstructions, non-uniform illumination by feedhorn asymmetry and alter strengths of sidelobes vs. central beam
• Emission received from pattern outside first sidelobe ring often called stray radiation
• FWHM of central beam is beamwidth
• Integrated solid angle of central beam is o
• Gain related to beam via G = 4 / o
Sensitivity
• Limited by noise – mostly thermal noise within electronics but also from ground reflected off telescope structure into feedhorn and CMB
• System temperature: temperature of blackbody producing same power as telescope + instrumentation produces when there is no source in beam
• Often give brightness of source in temperature units: difference in effective blackbody temperature when source is in beam vs. when no source is in beam – even when source is spectral line or synchrotron radiation and brightness has little to do with actual temperature of the source
• Preferred unit (requires calibration) is Jansky:
1Jy = 10-26 W m-2 Hz-1
• Limiting sensitivity for unpolarized source set by requiring signal added by source to equal rms uncertainty in Tsys:
S = 2kTsys Aeff-1 (B)-1/2
(k: Boltzmann’s constant; integration time)
• For spectral line work, B is set by velocity resolution required; Tsys and Aeff set by telescope and instumentation increase sensitivity by integrating longer – but need 4 times integration time to increase sensitivity by factor of 2
Polarization
• H I sources unpolarized, but synchrotron sources are often polarized to some extent – E in plane of electron’s acceleration
• Single receiver (LNA) can respond to only single polarization at any instant– either one component of linear polarization or one handedness of circular polarization
• So two receivers required to receive both polarizations
• Linear Ex and Ey with phase difference
• Stokes’ parameters:
I = Ex2 + Ey
2
Q = Ex2 Ey
2
U = 2ExEycos
V = 2ExEysin
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